Answer:
(15/2) sqrt(2)
Explanation:
The diagonal of a square divides the square into
two congruent isosceles right triangles, where we define
s to be the length of each of the sides of the square.
So, the diagonal is the hypotenuse of each of the isosceles
right triangles. Using either one of the right triangles, by
the Pythagorean Theorem, we have that
(the diagonal)^2 = s^2 + s^2
(15 cm)^2 = 2 s^2
225 cm^2 = 2 s^2
2 s^2 = 225 cm^2
sqrt(2) s = 15 cm
s = 15 cm/sqrt(2)
s = (15/2) sqrt(2) cm